Active damping of a piezoelectric tube scanner using self-sensing piezo actuation

Abstract

In most Atomic Force Microscopes (AFM), a piezoelectric tube scanner is used to position the sample underneath the measurement probe. Oscillations stemming from the weakly damped resonances of the tube scanner are a major source of image distortion, putting a limitation on the achievable imaging speed. This paper demonstrates active damping of these oscillations in multiple scanning axes without the need for additional position sensors. By connecting the tube scanner in a capacitive bridge circuit the scanner oscillations can be measured in both scanning axes, using the same piezo material as an actuator and sensor simultaneously. In order to compensate for circuit imbalance caused by hysteresis in the piezo element, an adaptive balancing circuit is used. The obtained measurement signal is used for feedback control, reducing the resonance peaks in both scanning axes by 18 dB and the cross-coupling at those frequencies by 30 dB.

Experimental results demonstrate a significant reduction in scanner oscillations when applying the typical triangular scanning signals, as well as a strong reduction in coupling induced oscillations. Recorded AFM images show a considerable reduction in image distortion due to the proposed control method, enabling artifact free AFM-imaging at a speed of 122 lines per second with a standard piezoelectric tube scanner.

Introduction

Atomic Force Microscopy (AFM) [1] is an important tool in nanotechnology to provide images up to atomic resolution under several environmental conditions. In AFM, the sample topography is measured by a very sharp tip which is mounted on the free end of a small cantilever beam, as depicted in Fig. 1. By probing the surface topography with the tip while the sample is scanned in a raster scan pattern, a topographical image of the sample is recorded. To provide the positioning of the sample in all three spatial directions, most commercially available AFM setups use piezoelectric tube scanners [2], as shown in Fig. 1, because of their simple design, high resolution and low cost. These tube scanners consist of a tube of piezoelectric material with segmented electrodes on the side. In order to provide the lateral scanning motion, a voltage is applied over the electrodes which induces a bending motion of the tube. One major drawback of these piezoelectric tube scanners, however, are their weakly damped resonances. Excitation of these resonances induces scanner oscillations, which is a major cause of image distortion in AFM-imaging [3], [4]. To prevent excitation of these oscillations the line scan rate is limited to about 1% of the scanners fundamental resonance frequency, making AFM-imaging a relatively time consuming process taking in the order of several minutes per image for conventional AFM setups [5], [6].

In literature several methods can be found to compensate for the scanner oscillations, which can be subdivided in feedforward and feedback control methods [7], [8]. With feedforward techniques the input signal is shaped such that the scanner resonances are not excited, which result in a significant enhancement of the achievable scan speed [3], [4], [9], [10]. Feedforward methods, however, do not apply direct damping to the scanners resonant modes, such that these may still be excited by environmental noise. Furthermore, feedforward methods are relatively sensitive for changes of the system dynamics, occurring for instance when changing the sample mass resulting in a shift of the resonance frequency [4].

Feedback control methods [11], [12], [13] can account for system uncertainty and allow active damping of the resonant modes. However, as conventional feedback control methods require the use of position sensors, e.g. capacitive or optical, application of feedback control is cost-intensive. In [14], [15] the use of external position sensors is omitted by using part of the available electrode surface of the piezoelectric tube for sensing, measuring the charge induced on these passive electrodes by the bending of the tube. Although this technique enables active damping of the fundamental resonances, the maximum scan range is compromised as not the whole available electrode surface is used for actuation. In [16], [17], a reduction of scanner oscillations is achieved by connecting a shunt impedance in parallel with the scan-electrodes. Although most of the contributions mentioned above are mainly concerned with compensation of the oscillations in the fast scanning axis, mechanical cross-couplings in the piezoelectric tube can induce oscillations in the slow scanning axis as well. This becomes even more evident when image rotation in applied, as in that case the fast and slow scanning directions are not in line with the position axes of the piezoelectric tube scanner.

In this contribution, self-sensing actuation and damping of both scanning axes of a piezoelectric tube scanner is presented, reducing the resonance peaks in both scanning axes as well as the resonance induced cross-coupling without the need for additional position sensors. In Sections 2 Self-sensing piezo actuation, 3 Bridge circuit imbalance compensation self-sensing actuation and a method to compensate for circuit imbalance are described. The design of the feedback controller for active damping of the scanner resonances is discussed in Section 4, and the implementation of the proposed control system is presented in Section 5. The achieved damping and higher scan speed is demonstrated experimentally in Section 6, showing a significant reduction in scanner oscillations at fast scanning. AFM images recorded at 122 lines per second demonstrate the significant reduction of the scanner oscillations and improvement in image quality.